The Sweden international's initial month-long stay at Pride Park expired after Saturday's 4-2 defeat by Queens Park Rangers, during which he was substituted due to a black eye.
Stoor will now return to Fulham, but Clough is keen to agree terms to keep the right-back at Derby until the New Year.
"His eye completely closed," said Clough.
"If you have seen the Rocky films, you'll know what I mean.
"He has a good black eye and there was no way he could continue but we are looking to extend his loan."
The 25-year-old made four appearances during his initial stint with the Rams, having featured just twice as a substitute in the Premier League for Fulham since joining from Rosenborg in 2008.